1. Field of the Invention
The invention relates to an optical system, and in particular to an optical system with a spatial filter to obtain traverse aberration of a test element.
2. Description of the Related Art
Since its development (Kirkham, The Ronchi test for mirrors, in Amateur Telescope Making. 1953. p. 264.) by the Italian Vasco Ronchi in 1923, professionals and amateur opticians have used the Ronchi test to evaluate surface figure errors in optics. Although there are other geometrical test methods, such as the Foucault and wire test, performed at or near the focal plane of an optical system, these methods do not quantify surface errors as well. Unlike the evolution in sophistication of interferometric testing methods, the Ronchi test has not been improved considerably from its original arrangement. Many laboratory institutions and optical shops still use the Ronchi test in its original form. The modified Ronchi test that uses an extended light source and a matching grating is also more than 50 years old. In some cases the Ronchi test is still considered to be the main apparatus for coarse surface testing before an interferometer is used for more precise measurement.
The Ronchi test has been primarily used in a qualitative approach rather than in a quantitative manner. The fringes observed in the Ronchi test convey qualitative information used to improve the figure of an optical surface. For example, by comparing actual test fringes with computer generated fringes, an experienced optician can guide and correct the figure of an optical surface. However, it is possible even for an experienced optician to misinterpret the Ronchi patterns and make figuring mistakes. Despite publication of methods to quantify the Ronchi test measurements, there are still no commercial quantitative Ronchi testers available.
The Ronchi test can be explained by using geometrical optics. The geometrical theory has been explained by Malacara and is based on transverse aberration theory. Transverse aberrations are related to the derivatives of the wavefront deformation at the exit pupil of the optical system under test.
With reference to FIG. 1, a simplified optical system with a wavefront deformation W at the exit pupil has a paraxial radius r. The transverse ray aberration at the observation plane is TAy.
The derivative of the wavefront deformation W(Xp,Yp) is related to the transverse ray aberrations TAy by the formula,
                                          ∂                          W              ⁡                              (                                                      X                    p                                    ,                                      Y                    p                                                  )                                                          ∂                          X              p                                      =                              -                          TA              y                                            r            -            W                                              (                  1          -          1                )            
For wavefront aberration, W, is very small compared with r and therefore W can be ignored, simplifying the formula to,
                                          ∂                          W              ⁡                              (                                                      X                    p                                    ,                                      Y                    p                                                  )                                                          ∂                          Y              p                                      =                              -                          TA              y                                r                                    (                  1          -          2                )            
Thus a simple formula is provided between the Y-component of the transverse ray aberration and the derivative of the wavefront. The quantity TAy is the Y-position where the ray intercepts the observation plane. The transverse ray aberration TAy is what can be measured by using the Ronchi test.
As shown in FIG. 2 in the traditional Ronchi test, a grating, either binary or sinusoidal, is placed at or near the paraxial focus of the aberrated beam. Dark fringes appear when the ray interception on the grating plane is coincident with a grating line so that light is blocked by the grating. The periodicity of the grating used in the Ronchi test permits quantification of the transverse ray aberration as conveyed by the fringes. Formula (1-3) describes light rays blocked by one of the grating's lines or dark bands,
                              TA          x                =                              r            ×                                          ∂                W                                            ∂                                  X                  p                                                              =          Nd                                    (                  1          -          3                )            
Where d is the pitch of the grating and N represents an integer. By analogy, if the grating is rotated by 90° to be parallel to the X-axis, dark fringes occur when,
                              TA          y                =                              r            ×                                          ∂                W                                            ∂                                  X                  p                                                              =          Nd                                    (                  1          -          4                )            
If the two transverse ray aberration functions TAx(Xp, Yp) and TAy(Xp, Yp) are known, integration generates the wavefront aberration W at the exit pupil, such that measurement of the transverse ray aberrations in both directions is sufficient to reconstruct the wavefront aberration.
If the grating is placed on a micrometer-stage, paraxial focus position and marginal focus position can be determined by scanning along the Z-axis, allowing rough quantification of the amount of spherical aberration and determination of correction measures.
Geometrical tests that measure transverse ray aberrations are capable of measuring large figure errors and thus are useful in evaluating ground surfaces. The optical testing of a rough and large optical surface has been a practical problem in the field of large optical surface fabrication. The testing of ground surfaces with short wavelengths in the visible spectrum presents problems due to the strong light scattering from the rough surface. A small rough optical surface can be tested by using a mechanical stylus profilometer or an optical profilometer. However, due to the size limitations of profilometers, data reduction, and testing time, an interferometric test using a carbon dioxide laser at 10.6 micrometers is an option often used for large surfaces (Kwon, O., J. C. Wyant, and C. R. Hayslett, Rough-Surface Interferometry at 10.6-Mu-M. Applied Optics, 1980. 19(11): p. 1862-1869; Munnerly. Cr and M. Latta, Rough Surface Interferometry Using a Co2 Laser Source. Applied Optics, 1968. 7(9): p. 1858-&). Nonetheless, the invisible wavelength and high power output of the carbon dioxide laser increases the difficulties of the optical testing. One way to perform visible wavelength interferometry or other testing methods, such as the Foucault or Ronchi test, on a rough surface is by waxing the ground surface to reduce light scattering therefrom. Wax is applied to the ground surface and allowed to dry, and then it is buffeted to obtain a specular coating that allows optical testing. Another technique utilizes varnishing of the optical surface. Two experiments were conducted by varnishing ground optical surfaces to verify that sufficient specular light was reflected from the varnished surface to allow an optical test to be performed.